Nothingness

Since metaphysics is the study of what exists, one might expect
metaphysicians to have little to say about the limit case in which
nothing exists. But ever since Parmenides in the fifth century BCE,
there has been rich commentary on whether an empty world is possible,
whether there are vacuums, and about the nature of privations and
negation.

This survey starts with nothingness at a global scale and then
explores local pockets of nothingness. Let's begin with a question that
Martin Heidegger famously characterized as the most fundamental issue
of philosophy.

Well, why not? Why expect nothing rather than something? No
experiment could support the hypothesis ‘There is nothing’
because any observation obviously implies the existence of an
observer.

Is there any a priori support for ‘There is
nothing’? One might respond with a methodological principle that
propels the empty world to the top of the agenda. For instance, many
feel that whoever asserts the existence of something has the burden of
proof. If an astronomer says there is water at the south pole of the
Moon, then it is up to him to provide data in support of the lunar
water. If we were not required to have evidence to back our existential
claims, then a theorist who fully explained the phenomena with one set
of things could gratuitously add an extra entity, say, a pebble outside our
light cone. We
recoil from such add-ons. To prevent the intrusion of superfluous
entities, one might demand that metaphysicians start with the empty
world and admit only those entities that have credentials. This is the
entry requirement imposed by Rene Descartes. He clears everything out and then
only lets back in what can be proved to exist.

St. Augustine had more conservative counsel: we should not start at
the beginning, nor at the end, but where we are, in the middle. We
reach a verdict about the existence of controversial things by
assessing how well these entities would harmonize with the existence of
better established things. If we start from nothing, we lack the
bearings needed to navigate forward. Conservatives, coherentists and
scientific gradualists all cast a suspicious eye on ‘Why is there
something rather than nothing?’.

Most contemporary philosophers feel entitled to postulate whatever
entities are indispensable to their best explanations of well accepted
phenomena. They feel the presumption of non-existence is only plausible
for particular existence claims. Since the presumption only applies on
a case by case basis, there is no grand methodological preference for
an empty world. Furthermore, there is no burden of proof when everybody
concedes the proposition under discussion. Even a solipsist agrees
there is at least one thing!

A more popular way to build a presumption in favor of nothingness is
to associate nothingness with simplicity and simplicity with
likelihood. The first part of this justification is plausible.
‘Nothing exists’ is simple in the sense of being an easy to
remember generalization. Consider a test whose questions have the form
‘Does x exist?’. The rule ‘Always answer
no!’ is unsurpassably short and comprehensive.

All roads are blocked to a philosophy which reduces
everything to the word ‘no.’ To ‘no’ there is
only one answer and that is ‘yes.’ Nihilism has no
substance. There is no such thing as nothingness, and zero does not
exist. Everything is something. Nothing is nothing. Man lives more by
affirmation than by bread. (1862, pt. 2, bk. 7, ch. 6).

As far as simplicity is concerned, there is a tie between the nihilistic rule
‘Always answer no!’ and the inflationary rule ‘Always
answer yes!’. Neither rule makes for serious metaphysics.

Even if ‘Nothing exists’ were the uniquely simplest
possibility (as measured by memorability), why should we expect that
possibility to be actual? In a fair lottery, we assign the same
probability of winning to the ticket unmemorably designated 321,169,681
as to the ticket memorably labeled 111,111,111.

Indeed, the analogy with a lottery seems to dramatically reverse the
presumption of non-existence. If there is only one empty world and many
populated worlds, then a random selection would lead us to expect a
populated world.

Peter van Inwagen (1996) has nurtured this statistical argument. In
an infinite lottery, the chance that a given ticket is the winner is 0.
So van Inwagen reasons that since there are infinitely many populated
worlds, the probability of a populated world is equal to 1. Although
the empty world is not impossible, it is as improbable as anything can
be!

For the sake of balanced reporting, van Inwagen should acknowledge
that, by his reasoning, the actual world is also as improbable as
anything can be. What really counts here is the probability of
‘There is something’ as opposed to ‘There is
nothing’.

Is this statistical explanation scientific? Scientists stereotypically
offer causal explanations—which are obviously useless for
‘Why is there is something rather than nothing?’. However,
Elliot Sober (1983) argues that scientists also accept “equilibrium
explanations”. These explain the actual situation as the outcome of
most or all of the possible initial states. There is no attempt to
trace the path by which the actual initial state developed into the
present situation. It suffices that the result is invariant. Why do I
have enough oxygen to breathe even though all the oxygen molecules
could have congregated in one corner my room? The physicist explains
that while this specific arrangement is just as likely as any other,
the overwhelming majority of arrangements do not segregate
oxygen.

Most philosophers would grant Peter van Inwagen's premise that there
is no more than one empty world. They have been trained to model the
empty world on the empty set. Since a set is defined in terms of its
members, there can be at most one empty set.

But several commentators on the nature of laws are pluralists about
empty worlds (Carroll 1994, 64). They think empty worlds can be sorted
in terms of the generalizations that govern them. Newton's first law of
motion says an undisturbed object will continue in motion in a straight
line. Aristotle's physics suggests that such an object will slow down
and tend to travel in a circle. The Aristotelian empty world differs
from the Newtonian empty world because different counterfactual
statements are true of it.

If variation in empty worlds can be sustained by differences in the
laws that apply to them, there will be infinitely many empty worlds.
The gravitational constant of an empty world can equal any real number
between 0 and 1, so there are more than countably many empty worlds.
Indeed, any order of infinity achieved by the set of populated possible
worlds will be matched by the set of empty worlds.

This is true even if we restrict attention to laws that preclude all
objects and therefore only govern empty worlds. Consider a law that
requires any matter to adjoin an equal quantity of anti-matter. The
principles of matter and anti-matter ensure that they cannot co-exist
so the result would be an empty world.

Advocates of the fine tuning argument (a descendent of the design
argument) claim that the conditions under which life can develop are so
delicate that the existence of observers indicates divine intervention.
A similar argument might be fashioned that stresses what a narrow
range of laws permit the formation of concrete entities. From the
perspective of these fine tuners, the existence of a universe with
rocks is an inspiring surprise.

Some existentialists picture nothingness as a kind of force that
impedes each object's existence. Since there is something rather than
nothing, any such nihilating force cannot have actually gone unchecked.
What could have blocked it? Robert Nozick (1981, 123) toys with an
interpretation of Heidegger in which this nihilating force is
self-destructive. This kind of double-negation is depicted in the
Beatles's movie The Yellow Submarine. There is a creature that
zooms around like a vacuum cleaner, emptying everything in its path.
When this menace finally turns on itself, a richly populated world pops
into existence.

Some cultures have creation myths reminiscent of The Yellow
Submarine. Heidegger would dismiss them as inappropriately
historical. ‘Why is there something rather than nothing?’
is not about the origin of the world. Increasing the scientific
respectability of the creation story (as with the Big Bang hypothesis)
would still leave Heidegger objecting that the wrong question is being
addressed.

Some would disagree with van Inwagen's assumption that each possible
world is as likely as any other. There have been metaphysical systems
that favor less populated worlds.

Gottfried Leibniz pictured possible things as competing to become
actual. The more a thing competes with other things, the more likely
that there will be something that stops it from becoming real.
The winners in Leibniz's struggle for existence are cooperative. They
uniquely fit the niche formed by other things. Thus this key hole
into existence implicitly conveys information about everything.
The little bit that is not, tells us about all that there is.

On the one hand, this metaphysical bias in favor of simplicity is
heartening because it suggests that the actual world is not too complex
for human understanding. Scientists have penetrated deeply into the
physical world with principles that emphasize simplicity and
uniformity: Ockham's razor, the least effort principle, the anthropic
principle, etc.

On the other hand, Leibniz worried that the metaphysical bias
for simplicity, when driven to its logical conclusion, yields the
embarrassing prediction that there is nothing. After all, an empty
world would be free of objects trying to elbow each other out. It is
the easiest universe to produce. (Just do nothing!) So why is there is
something rather than nothing?

Leibniz's worry requires a limbo between being and
non-being. If the things in this limbo state do not really exist, how
could they prevent anything else from existing?

Leibniz's limbo illustrates an explanatory trap. To explain why
something exists, we standardly appeal to the existence of something
else. There are mountain ranges on Earth because there are plates on
its surface that slowly collide and crumple up against each other.
There are rings around Saturn because there is an immense quantity of
rubble orbiting that planet. This pattern of explanation is not
possible for ‘Why is there something rather than nothing’.
For instance, if we answer ‘There is something because the
Universal Designer wanted there to be something’, then our
explanation takes for granted the existence of the Universal Designer.
Someone who poses the question in a comprehensive way will not grant
the existence of the Universal Designer as a starting point.

If the explanation cannot begin with some entity, then it is hard to
see how any explanation is feasible. Some philosophers conclude
‘Why is there something rather than nothing?’ is
unanswerable. They think the question stumps us by imposing an
impossible explanatory demand, namely, Deduce the existence of
something without using any existential premises. Logicians should
feel no more ashamed of their inability to perform this deduction than
geometers should feel ashamed at being unable to square the circle.

David Hume offers a consolation prize: we might still be able
explain the existence of each event even if it is impossible to explain
everything all together. Suppose that the universe is populated with an
infinite row of dominoes. The fall of each domino can be explained by
the fall of its predecessor.

Hume denied that the existence of anything could be proved by reason
alone. But rationalists have been more optimistic. Many have offered
a priori proofs of God's existence. Such a proof would double
as an explanation of why there is something. If God exists, then
something exists. After all, God is something.

But would God be the right sort of something? If we are only seeking
an a priori proof of something (anything at all!),
then why not rest content with a mathematical demonstration that there
exists an even prime number?

Van Inwagen's answer is that we are actually interested in
concrete things. A concrete entity has a position in space or
time. For instance, a grain of sand, a camel, and an oasis are all
concrete entities. Since they have locations, they have boundaries with their
environment. (The only exception would be an entity that took up all space and time.)

Admittedly, points in space and time have locations. But concrete
entities are only accidentally where and when they are. All concrete
entities have intrinsic properties. Their natures are not exhausted by
their relationships with other things. Consider Max Black's universe
containing nothing but twin iron spheres. The spheres are distinct yet
have the same relationships and the same intrinsic properties.

All material things are concrete but some concrete things
might be immaterial. Shadows and holes have locations and durations but
they are not made of anything material. There is extraneous light in
shadows and extraneous matter in holes; but these are contaminants
rather than constituents. If there are souls or Cartesian minds, then
they will also qualify as immaterial, concrete entities. Although they
do not take up space, they take up time. An idealist such as George
Berkeley could still ask ‘Why is there is something rather than
nothing?’ even though he was convinced that material things are
not possible.

Although all concrete things are in space or time, neither space nor
time are concrete things. Where would space be? When would time occur?
These questions can only be answered if space were contained in
another higher space. Time would be dated within another time. Since
the same questions can be posed for higher order space and higher
order time, we would face an infinite regress.

There is no tradition of wondering ‘Why is there space and
time?’. One reason is that space and time seem like a framework
for there being any contingent things.

Absolutists think of the framework as existing independently of what
it frames. For instance, Newton characterized space as an eternal,
homogenous, three dimensional container of infinite extent. He
believed that the world was empty of objects for an infinite period
prior to creation (setting aside an omnipresent God). An empty world
would merely be a continuation of what creation interrupted.

Others think the framework depends on what it frames. Like Leibniz,
Albert Einstein pictured (or “pictured”) space as an abstraction from
relations between objects. Consequently, space can be described with
the same metaphors we use for family trees. Maybe space grows
bigger. Maybe space is curved or warped or has holes. There is much
room to wonder why space has properties that it has. But since space
is an abstraction from objects, answers to any riddles about space
reduce to facts about objects. One can wonder why there is space. But
this is only to wonder why there are objects.

All concrete things appear to be contingent beings. For instance,
the Earth would not have existed had the matter which now constitutes
our solar system formed, as usual, two stars instead of one. If no
concrete thing is a necessary being, then none of them can explain the
existence of concrete things.

Even if God is not concrete, proof of His existence would raise hope
of explaining the existence of concrete things. For instance, the
Genesis creation story suggests that God made the Earth and
that He had a reason to do so. If this account could be corroborated we
would have an explanation of why the Earth exists and why we exist.

This divine explanation threatens to over-explain the data. Given
that God is a necessary being and that the existence of God
necessitates the existence of the Earth, then the Earth would be a
necessary being rather than a contingent being.

The dilemma was generalized by William Rowe (1975). Consider all the
contingent truths. The conjunction of all these truths is itself a
contingent truth. On the one hand, this conjunction cannot be explained
by any contingent truth because the conjunction already contains all
contingent truths; the explanation would be circular. On the other
hand, this conjunction cannot be explained by a necessary truth because
a necessary truth can only imply other necessary truths. This dilemma
suggests that ‘Why are there any contingent beings?’ is
impossible to answer.

Rowe is presupposing that an answer would have to be
a deductive explanation. If there are ‘inferences to
the best explanation’ or inductive explanations, then there
might be a way through the horns of Rowe's dilemma.

There also remains hope that Rowe's dilemma can be bypassed by showing
that the empty world is not a genuine possibility. Then the retort to
‘Why is there something rather than nothing?’ is
‘There is no alternative to there being something’.

‘There might be nothing’ is false when read
epistemically. (Roughly, a proposition is epistemically possible if it
is consistent with everything that is known.) For we know that
something actually exists and knowledge of actuality
precludes epistemic possibility. But when read metaphysically,
‘There might be nothing’ seems true. So ‘Why is
there something rather than nothing?’ is, so far, a live
question.

The question is not undermined by the a priori status of
knowledge that something exist. (I know a priori that
something exists because I know a priori that I exist and
know this entails ‘Something exists’.) Knowledge, even
a priori knowledge, that something is actually true is
compatible with ignorance as to how it could be true.

Residual curiosity is possible even when the the proposition is known
to be a necessary truth. A reductio ad absurdum proof that 1
− 1/3 + 1/5 − 1/7 + … converges to π/4 might
persuade me that there is no alternative without illuminating how it
could be true. For this coarse style of proof does not explain how π
wandered into the solution. (Reductio ad absurdum just shows
a contradiction would follow if the conclusion were not true.) This raises the possibility that even a
logical demonstration of the metaphysical necessity of
‘Something exists’ might still leave us asking why there
is something rather than nothing (though there would no longer be the
wonder about the accidentality of there being something).

Henri Bergson maintained that nothingness is precluded by the
positive nature of reality. The absence of a female pope is not a brute
fact. ‘There is not a female pope’ is made true by a
positive fact such as the Catholic Church's regulation that all priests
be men and the practice of drawing popes from the priesthood. Once we
have the positive facts and the notion of negation, we can derive all
the negative facts. ‘There is nothing’ would be a
contingent, negative fact. But then it would have to be grounded on
some positive reality. That positive reality would ensure that there is
something rather than nothing.

Human beings have a strong intuition that positive truths, such as
‘Elephants are huge’ are more fundamental than negative
truths such as ‘Elephants do not jump’. The robustness of
this tendency makes negative things objects of amusement. Consider the
Professor's remark during his chilly banquet in Lewis Carroll's
Sylvie and Bruno Concluded.

“I hope you'll enjoy the dinner—such as it is; and
that you won't mind the heat—such as it isn't.”

How can we perceive absences? They seem causally inert and so not
the sort of thing that we could check empirically. Negative truths seem
redundant; there are no more truths than those entailed by the
conjunction of all positive truths. The negative truths seem
psychological; we only assert negative truths to express a frustrated
expectation. When Jean Paul Sartre (1969, 41) arrives late for his
appointment with Pierre at the cafe, he sees the absence of Pierre but
not the absence of the Duke of Wellington.

Philosophers have had much trouble vindicating any of these
intuitions. Bertrand Russell (1985) labored mightily to reduce negative
truths to positive truths. Russell tried paraphrasing ‘The cat is
not on the mat’ as ‘There is a state of affairs
incompatible with the cat being on the mat’. But this paraphrase
is covertly negative; it uses ‘incompatible’ which means
not compatible. He tried modeling ‘Not
p’ as an expression of disbelief that p. But
‘disbelief’ means believing that something is not
the case. Is it even clear that absences are causally inert? Trapped
miners are killed by the absence of oxygen. In the end Russell gave up.
In a famous lecture at Harvard, Russell concluded that irreducibly
negative facts exist. He reports this nearly caused a riot.

Were it not for the threat to social order, one might stand the
intuition on its head: Negative truths are more fundamental than
positive truths. From a logical point of view, there is greater promise
in a reduction of positive truths to negative truths. Positive truths
can be analyzed as the negations of negative truths or perhaps as
frustrated disbelief. Positive truths would then be the redundant
hanger-ons, kept in circulation by our well-documented difficulty in
coping with negative information. Think of photographic negatives. They
seem less informative than positive prints. But since the prints are
manufactured from the negatives, the negatives must be merely more
difficult for us to process.

As difficult as negation might be psychologically, it is easier to
work with than the alternatives suggested by Henry Sheffer. In 1913,
he demonstrated that all of the logical connectives can be defined in
terms of the stroke function |. It is the dual of conjunction: p|q is
false exactly when p and q are each true. The same goes for the dual
of disjunction, the dagger function, which is true exactly when p and
q are each false. From a logical point of view, negation is
dispensable. This raises hope that all of the paradoxes of negation
can be translated away.

Bertrand Russell quickly incorporated the stroke function
into Principia Mathematica. Sheffer's functions have also
been a great economy to computers (as witnessed by the popularity of
NAND gates). However, human beings have trouble achieving fluency
with Sheffer's connectives. Even Sheffer
translates p|q as neither p
nor q. Psychologically, this is a double dose of negation
rather than an alternative to negation.

But we could let computers do our metaphysics just as we let them do
our taxes. The only serious objection is that the problems of
negation do not really go away when we translate into artificial
languages. For instance, the challenge posed by negative existential
sentences such as ‘Pegasus does not exist’ persists when
it is translated with a Sheffer stroke into ‘Pegasus
exists|Pegasus exists’. Any desire to make ‘Pegaus does
not exist’ come out true warrants a desire to make
‘Pegasus exists|Pegasus exists’ come out true. (Since
classical logic does not permit empty names, the stroke existential
sentence will be false.)

The more general concern is that the problems which are naturally
couched in terms of negation persist when they are translated into a
different logical vocabulary. Given that the translation preserves
the meaning of the philosophical riddle, it will also preserve its
difficulty.

We will engage in negative thinking to avoid highly complicated
positive thinking. What is the probability of getting at least one
head in ten tosses of a coin? Instead of directly computing the
probability of this highly disjunctive positive event, we switch to a
negative perspective. We first calculate the probability of an absence
of heads and then exploit the complement rule: Probability (at least
one head) = 1 − Probability (no heads).

Some possible worlds are easier to contemplate negatively. Thales
said that all is water. Suppose he was nearly right except for the
existence of two bubbles. These two absences of water become the
interesting players (just as two drops of water in an otherwise empty
space become interesting players in the dual of this universe). How
would these bubbles relate to each other? Would the bubbles repel each other?
Would the bubbles be mutually unaffected? Deep thinking about gravity yields
the conclusion that the bubbles would attract each other! (Epstein
1983, 138-9)

The hazard of drawing metaphysical conclusions from psychological
preferences is made especially vivid by caricatures. We know that
caricatures are exaggerated representations. Despite the flagrant
distortion (and actually because of it) we more easily recognize
people from caricatures rather than from faithful portraits.

For navigational purposes, we prefer schematic subway maps over ones
that do justice to the lengths and curves of the track lines. But this
is not a basis for inferring that reality is correspondingly schematic.

Our predilection for positive thinking could reflect an objective
feature of our world (instead of being a mere anthropocentric
projection of one style of thought). But if this objective
positiveness is itself contingent, then it does not explan why there
is something rather than nothing. For Bergson's explanation to
succeed, the positive nature of reality needs to be a metaphysically
necessary feature.

Thomas Baldwin (1996) reinforces the possibility of an
empty world by refining the following thought experiment: Imagine a world
in which there are only finitely objects. Suppose each object
vanishes in sequence. Eventually you run down to three objects, two
objects, one object and then Poof! There's your empty
world.

What can be done temporally can be done modally. There is only a small
difference between a world with a hundred objects and a world with
just ninety-nine, and from there …. well, just do the arithmetic!

Gonzalo Rodriguez (1997, 163) warns that we must subtract the right
way. Assume that each part of a concrete entity is itself
concrete. Also assume that concrete entities are infinitely divisible
(as seems natural given that space is dense). An infinitely complex
object cannot be nibbled away with any number of finite bites.

Our metaphysical calculations are subtly influenced by how we picture
possible worlds (Coggins 2003). If possible worlds are envisaged as
containers, then they can be completely emptied out. Similarly, if
possible worlds are pictured as stories (say maximally consistent ways
things could have been), then our library will contain a tale lacking
any concrete entities as characters. But if a possible worlds are
pictured mereologically, as giant composites of concrete objects
(Lewis 1986), our subtraction falters before we reach zero. Similarly,
if possible worlds require an active construction (say, Ludwig
Wittgenstein's imaginary rearrangements of objects drawn from the
actual world), then the very process of construction ensures that
there are some concrete objects in every possible world.

Some kind of background theory of possible worlds is needed. For
without this substantive guidance, the subtraction argument seems
invalid. More specifically, from a metaphysically neutral perspective,
the fact that it is possible for each object to not exist seems
compatible with it being necessary that at least one object
exists.

The founder of modal logic, Aristotle, has special reason to deny that
‘Necessarily (p or q)’ entails
‘Necessarily p or necessarily
q’. Aristotle believed that all abstract entities
depend on concrete entities for their existence. Yet he also believed
that there are necessary truths. The existence any particular
individual is contingent but it is necessary that some individuals
exist.

Science textbooks teem with contingent abstract entities: the
equator, Jupiter's center of gravity, NASA's space budget, etc.
Twentieth century mathematics makes sets central. Sets are defined in
terms of their members. Therefore, any set that contains a contingent
entity is itself a contingent entity. The set that contains you is an
abstract entity that has no weight or color or electric charge. But it
still depends on you for its existence.

Mathematics can be reconstructed in terms of sets given the
assumption that something exists. From you we derive the set containing
you, then the set containing that set, then the set containing that
larger set, and so on. Through ingenious machinations, all of
mathematics can be reconstructed from sets. Contemporary set theorists
like to spin this amazing structure from the empty set so as to not
assume the existence of contingent beings. This is the closest
mathematicians get to creation from nothing!

Early set theorists and several contemporary metaphysicians reject
the empty set. Yet the loveliness of the construction makes many
receptive to Wesley Salmon's ontological argument: “The fool saith in
his heart that there is no empty set. But if that were so, then the set
of all such sets would be empty, and hence it would be the
empty set.”

E. J. Lowe argues on behalf of the fool: “A set has these
[well-defined identity conditions] only to the extent that its members
do—but the empty set has none. Many things have no
members: what makes just one of these qualify as ‘the
empty set’” (1996, 116 fn.) Since mathematical statements such as
‘The first prime number after 1,000,000 is 1,000,003’ are
necessary truths and can only be rendered true by the existence of a
contingent being, Lowe concludes that there necessarily exists at least
one contingent being. In other words, the empty world is impossible
even if there are no necessary beings.

There are other metaphysical systems that make the existence of some
concrete entities necessary without implying that there are any
necessarily existing concrete things. In his Tractatus phase,
Ludwig Wittgenstein takes a world to be a totality of facts. A fact
consists of one or more objects related to each other in a certain
way. By an act of selective attention, we concentrate on just the
objects or just the relations. But objects and relations are always
inextricably bound up with each other. Since every fact requires at
least one object, a world without objects would be a world without
facts. But a factless world is a contradiction in terms. Therefore,
the empty world is impossible.

Nevertheless, the persuasiveness of the subtraction argument is not
entirely hostage to background theories about the nature of possible
worlds. Even those with metaphysical systems that guarantee the
existence of some concrete entities feel pressure to revise those
systems to accommodate the empty world, or at least to look for some
loophole that would make their system compatible with Baldwin's
thought experiment.

Consider the combinatorialist David Armstrong. He recently acquisced
to the empty world by relaxing his account of truthmakers. A
truthmaker is a piece of reality that makes a statement true.
Armstrong believes that every contingent truth is made true by a
truthmaker and has wielded the principle forcefully against analytical
behaviorists, phenomenalists, nominalists, and presentists. Since
there can be no truthmaker for an empty world, Armstrong appears to
have a second objection to the empty world (supplementing the
objection based on his combinatorial conception of a possible
world). Yet Armstrong (2004, 91) instead claims that the empty world
could borrow truthmakers from the actual world. His idea is that the
truthmakers for possibilities are actual objects and that these actual
objects could serve as the truthmakers for the empty world. David
Erfid and Tom Stoneham (2009) object that cross-world truthmakers
would be equally handy to the analytical behaviorists, phenomenalists
and their ilk. Whether or not Armstrong has contradicted himself, he
has illustrated the persuasiveness of the subtraction argument.

Aristotle assumes that universal generalizations have existential
import; ‘All men are mortal’ implies that there are men.
But consider linked quantifications such as ‘All trespassers
will be shot. All survivors will be shot again.’ The conjunction
of these two universal generalizations is not a contradiction. The
conjunction is false if there is a wounded trespasser who fails to be
re-shot. But it can be true if all potential trespassers heed the
warning. The force of the warning is conditional; ‘IF there is a
trespasser, THEN he will be shot. And IF he survives this shooting,
THEN he will be shot again.’

Twentieth century logicians were impressed by generalizations such as
‘All immortals live forever’ that do not commit to the
existence of the subject items. They also wanted to preserve the
intuitive equivalence between ‘All men are mortal’ and its
contrapositive ‘All immortals are non-men’. They analyzed
universal generalizations as conditionals: ‘All men are
mortal’ means ‘For each x, if x is a
man, then x is mortal’. If there are no men, then the
generalization is vacuously true. Nevertheless, the logicians still
insisted that the universal quantifier has existential import; if all
is water, then there exists some water.

Even with this revision, classical logic militates against the empty world. Since its
universal quantifier has existential import, each of its logical laws
imply that something exists. For instance, the principle of identity,
Everything is identical to itself entails There exists
something that is identical to itself. All sorts of attractive
inferences are jeopardized by the empty world.

Logicians do not treat their intolerance of the empty world as a
resource for metaphysicians. They do not want to get involved in
metaphysical disputes. They feel that logic should be neutral with
respect to the existence of anything. They yearn to rectify this
“defect in logical purity” (Russell 1919, 203).

The ideal of ontological neutrality has led some philosophers to
reject classical logic. A direct response would be to be challenge the
existential import of the classical quantifiers.

Proponents of “free
logic” prefer to challenge the existential presupposition of singular
terms (Lambert 2003, 124). In classical logic, names must have
referents. Free logic lacks this restriction and so countenances empty
names as in ‘Sherlock Holmes is a detective’ and negative existentials
such as ‘Pegasus does not exist’.

These changes would have implications for W. V. Quine's (1953a) popular
criterion for ontological commitment. Quine says that we can read off
our ontology from the existentially quantified statements constituting
our well-accepted theories. For instance, if evolutionary theory says
that there are some species that evolved from other species, and if we
have no way to paraphrase away this claim, then biologists are
committed to the existence of species. Since philosophers cannot
improve on the credentials of a scientific commitment, metaphysicians
would also be obliged to accept species.

So how does Quine defend his criterion of ontological commitment
from the menace looming from the empty domain? By compromise. Normally
one thinks of a logical theorem as a proposition that holds in all
domains. Quine (1953b, 162) suggests that we weaken the requirement to
that of holding in all non-empty domains. In the rare circumstances in
which the empty universe must be considered, there is an easy way of
testing which theorems will apply: count all the universal
quantifications as true, and all the existential quantifications as
false, and then compute for the remaining theorems.

Is Quine being ad hoc? Maybe. But exceptions are common for
notions in the same family as the empty domain. For instance,
instructors halt their students' natural pattern of thinking about
division to forestall the disaster that accrues from permitting
division by zero. If numbers were words, zero would be an irregular
verb.

Many of the arguments used to rule out total emptiness also preclude
small pockets of emptiness. Leibniz says that the actual world must
have something rather than nothing because the actual world must be the
best of all possible worlds, and something is better than nothing. But
by the same reasoning, Leibniz concludes there are no vacuums in the
actual world: more is better than less.

Leibniz also has arguments that target the possibility
of there being more than one void. If there could be more than one
void, then there could be two voids of exactly the same shape and size.
These two voids would be perfect twins; everything true of one void
would be true of the other. This is precluded by the principle of the
identity of indiscernibles: if anything true of x is true of
y, then x is identical to y.

A second problem with multiple voids arises from efforts to
paraphrase them away. From the time of Melissus, there have been
arguments against the possibility of a void existing in the manner that
an object exists: “Nor is there any void, for void is nothing, and
nothing cannot be.” (Guthrie 1965, 104) If you say there is a vacuum in
the flask, then you are affirming the existence of something in the
flask—the vacuum. But since ‘vacuum’ means an
absence of something, you are also denying that there is something in
the flask. Therefore, ‘There is a vacuum in the flask’ is a
contradiction.

Some react to Melissus's argument by analyzing vacuums as properties
of things rather than things in their own right. According to C. J. F.
Williams (1984, 383), ‘There is a vacuum in the flask’
should be rendered as ‘The flask noths’. He does this in
the same spirit that he renders ‘There is fog in
Winchester’ as ‘Winchester is foggy’ and
‘There is a smell in the basement’ as ‘The basement
smells’.

If this paraphrase strategy works for vacuums, it ought to work for
the more prosaic case of holes. Can a materialist believe that there
are holes in his Swiss cheese? The holes are where the matter is not. So to
admit the existence of holes is to admit the existence of immaterial
objects!

One response is to paraphrase ‘There is a hole in the
cheese’ as ‘The cheese holes’ or, to be a bit easier
on the ear, as ‘The cheese is perforated’. What appeared to
be an existential claim has metamorphosized into a comment on the shape of the
cheese.

But how are we to distinguish between the cheese having two holes as
opposed to one? (Lewis and Lewis 1983, 4) Well, some cheese is singly
perforated, some cheese is doubly-perforated, yet other cheese is
n-perforated where n equals the number of holes in
the cheese.

Whoa! We must be careful not to define
‘n-perforation’ in terms of holes; that would
re-introduce the holes we set out to avoid.

Can holes be avoided by confining ourselves to the process of perforation?
Single-hole punchers differ from triple-hole punchers by how they act; singlely
rather than triply.

The difficulty with this process-oriented proposal that the product, a hole, is needed to distinguish between successful
and merely attempted perforation. Furthermore, the paraphrase is incomplete because it does not extend to unmade holes.

Can we just leave expressions of the form
‘n-perforated’ as primitive, unanalyzed shape
predicates? The Lewises note that this strands us with an infinite list of primitive
terms. Such a list could never have been memorized. The Lewises do not
see how ‘n-perforated’ can be recursively defined
without alluding to holes.

The paraphrase prospects seem equally bleak for being
‘n-vacuumed’. Big meteorites pass through the
atmosphere in about one second leaving a hole in the
atmosphere—a vacuum in “thin air”. The air cannot
rush in quickly enough to fill the gap. This explains why rock vapor
from the impact shoots back up into the atmosphere and later rains
down widely on the surface. During a meteorite shower, the atmosphere
is multiply vacuumed. But this is just to say that there are many
vacuums in the atmosphere.

The trouble sustaining multiple voids may push us to the most
extreme answer to ‘Why is there something rather than
nothing?’, namely, ‘There must not only be something but
there must not be any emptiness at all!’.

Parmenides maintained that it is self-defeating to say that
something does not exist. The linguistic rendering of this insight is
the problem of negative existentials: ‘Atlantis does not
exist’ is about Atlantis. A statement can be about something only
if that something exists. No relation without relata! Therefore,
‘Atlantis does not exist’ cannot be true. Parmenides and
his disciples elaborated conceptual difficulties with negation into an
incredible metaphysical monolith.

The Parmenideans were opposed by the atomists. The atomists said
that the world is constituted by simple, indivisible things moving in
empty space. They self-consciously endorsed the void to explain
empirical phenomena such as movement, compression, and absorption.

Parmenides's disciple, Zeno of Elea, had already amassed an amazing
battery of arguments to show motion is impossible. Since these imply
that compression and absorption are also impossible, Zeno rejects the
data of the atomists just as physicists reject the data of parapsychologists.

Less radical opponents of vacuums, such as Aristotle, re-explained
the data within a framework of plenism: although the universe is full,
objects can move because other objects get out of the way. Compression
and absorption can be accommodated by having things pushed out of the way
when other things jostle their way in.

Aristotle denied the void can explain why things move. Movement
requires a mover that is pushing or pulling the object. An object in a
vacuum is not in contact with anything else. If the object did move,
there would be nothing to impede its motion. Therefore, any motion in a
vacuum would be at an unlimited speed.

Aristotle's refutation of the void persuaded most commentators for
the next 1500 years. There were two limited dissenters to his thesis
that vacuums are impossible. The Stoics agreed that terrestrial vacuums
are impossible but believed there must be a void surrounding the
cosmos. Hero of Alexandria agreed that there are no naturally occuring
vacuums but believed that they can be formed artificially. He cites
pumps and siphons as evidence that voids can be created. Hero believed
that bodies have a natural horror of vacuums and struggle to prevent
their formation. You can feel the antipathy by trying
to open a bellows that has had its air hole plugged. Try as you might,
you cannot separate the sides. However, unlike Aristotle, Hero thought
that if you and the bellows were tremendously strong, you could
separate the sides and create a vacuum.

Hero's views became more discussed after the Church's
anti-Aristotelian condemnation of 1277 which required Christian
scholars to allow for the possibility of a vacuum.

Christians are selective about which parts of the Bible to take seriously.
They do not always choose the easier assertions. A striking example is the
doctrine of creation from nothing. This jeopardized their overarching commitment
to avoid outright irrationality.
If creation out of
nothing were indeed a demonstrable impossibility, then faith would be forced to override an answer
given by reason
rather than merely answer a question about which reason is silent.

All Greek philosophy had assumed creation was from something more primitive,
not nothing. Consistently, the Greeks assumed destruction was disassembly
into more basic units. (If destruction into nothingness were possible, the
process could be reversed to get creation from nothing.) The Christians were
on their own when trying to make sense of creation from nothing.

Creation out of nothing presupposes the possibility of total nothingness.
This in turn implies that there can be some nothingness. Thus Christians
had a motive to first establish the possibility of a little nothingness.
Their strategy was start small and scale up.

Accordingly, scholars writing in the aftermath of the condemnation of 1277
proposed various recipes for creating vacuums. One scheme was to
freeze a sphere filled with water. After the water contracted into
ice, a vacuum would form at the top.

Aristotelians replied that the sphere would bend at its weakest point.
When the vacuists stipulated that the sphere was perfect, the rejoinder
was that this would simply prevent the water from turning into ice.

Neither side appears to have tried out the recipe. If either had, then
they would have discovered that freezing water expands rather than
contracts.

To contemporary thinkers, this dearth of empirical testing is bizarre.
The puzzle is intensified by the fact that the medievals did empirically
test many hypotheses, especially in optics.

Hero was eventually refuted by experiments with barometers conducted
by Evangelista Torricelli and Blaise Pascal. Their barometer consisted
of a tube partially submerged, upside down in bowl of mercury. What
keeps the mercury suspended in the tube? Is there an unnatural vacuum
that causes the surrounding glass to pull the liquid up? Or is there no
vacuum at all but rather some rarefied and invisible matter in the
“empty space”? Pascal answered that there really was nothing holding up
the mercury. The mercury rises and falls due to variations in the
weight of the atmosphere. The mercury is being pushed up the
tube, not pulled up by anything.

When Pascal offered this explanation to the plenist Descartes, Descartes wrote
Christian Huygens that Pascal had too much vacuum in his head.
Descartes identified bodies with extension and so had no room for
vacuums. If there were nothing between two objects, then they would be
touching each other. And if they are touching each other, there is no
gap between them.

Well maybe the apparent gap is merely a thinly occupied region of
space. On this distributional model, there is no intermediate “empty
object” that separates the two objects. There is merely unevenly spread
matter. This model is very good at eliminating vacuums in the sense of
empty objects. However, it is also rather good at eliminating ordinary
objects. What we call objects would just be relatively thick deposits
of matter. There would be only one natural object: the whole universe.
This may have been the point of Spinoza's attack on vacuums (Bennett
1980).

Descartes was part of a tradition that denied action at a distance.
Galileo was disappointed by Johannes Kepler's hypothesis that the moon
influences the tides because the hypothesis seems to require causal
chains in empty space. How could the great Kepler believe something so
silly? When Isaac Newton resurrected Kepler's hypothesis he was careful
to suggest that the space between the moon and the Earth was filled with
ether.

Indeed, the universality of Newton's law of gravitation seems to
require that the whole universe be filled with a subtle substance.
How else could the universe be bound together by causal chains?
Hunger for ether intensified as the wave-like features of light became
established. It is tautologous that a wave must have a medium.

Or is it? As the theoretical roles of the ether proliferated,
physicists began to doubt there could be anything that accomplished
such diverse feats. These doubts about the existence of ether were
intensified by the emergence of Einstein's theory of relativity. He
presented his theory as a relational account of space; if there were no
objects, there would be no space. Space is merely a useful abstraction.

Even those physicists who wished to retain substantival space broke
with the atomist tradition of assigning virtually no properties to the
void. They re-assign much of ether's responsibilities to space itself.
Instead of having gravitational forces being propagated through the
ether, they suggest that space is bent by mass. To explain how space
can be finite and yet unbounded, they characterize space as spherical.
When Edwin Hubble discovered that heavenly bodies are traveling away
from each other (like sleepy flies resting on an expanding balloon),
cosmologists were quick to suggest that space may be expanding.
“Expanding into what?” wondered bewildered laymen,
“How can space bend?”, “How can space have a
shape?”, ….

Historians of science wonder whether the ether that was loudly pushed
out the front door of physics is quietly returning through the back
door under the guise of “space”. Quantum field theory
provides especially fertile area for such speculation. Particles are
created with the help of energy present in “vacuums”. To
say that vacuums have energy and energy is convertible into mass, is
to deny that vacuums are empty. Many physicists revel in the discovery
that vacuums are far from empty.

Are these physicists using ‘vacuum’ in a new sense? If
they are trying to correct laymen, then they need to couch their
surprises in sentences using the ordinary sense of
‘vacuum’. Laymen are generally willing to defer to
scientists when they are characterizing natural kinds. But vacuums do
not seem like natural kinds such as the elements of the periodic table. They are not substances.

After a mystical experience in 1654, Blaise Pascal's interest in
nothingness passed from its significance to science to the significance
of nothingness to the human condition. Pascal thinks human beings have a unique
perspective on their finitude. His Pensees is a roller coaster
ride surveying the human lot. Pascal elevates us to the level of angels
by exalting in our grasp of the infinite, and then runs us down below
the beasts for wittingly choosing evil over goodness. From this valley of depravity
Pascal takes us
up again by marveling at how human beings tower over the microscopic
kingdom, only to plunge us down toward insignificance by having us
dwell on the vastness of space, and the immensity of eternity.

He who regards himself in this light will be afraid of
himself, and observing himself sustained in the body given him by
nature between those two abysses of the Infinite and Nothing, will
tremble at the sight of these marvels; and I think that, as his
curiosity changes into admiration, he will be more disposed to
contemplate them in silence than to examine them with presumption.

For in fact what is man in nature? A Nothing in comparison with the
Infinite, an All in comparison with the Nothing, a mean between nothing
and everything. Since he is infinitely removed from comprehending the
extremes, the end of things and their beginning are hopelessly hidden
from him in an impenetrable secret; he is equally incapable of seeing
the Nothing from which he was made, and the Infinite in which he is
swallowed up. (Pensees sect. II, 72)

Pascal's association of nothingness with insignificance and
meaninglessness presages themes popularized by existentialists after
World War II.

There are other important precursors. In The Concept of Dread, Soren Kierkegaard (1844) claims that
nothingness wells up into our awareness through moods and emotions.
Emotions are intentional states; they are directed toward something. If
angered, I am angry at something. If amused, there is
something I find amusing. Free floating anxiety is often cited as a
counterexample. But Kierkegaard says that in this case the emotion is
directed at nothingness.

According to Heidegger, we have several motives to shy away from the
significance of our emotional encounters with nothingness. They are
premonitions of the nothingness of death. They echo the groundlessness
of human existence.

Some have hoped that our recognition of our rootlessness would
rescue meaningfulness from the chaos of nothing. But Heidegger denies
us such solace.

Heidegger does think freedom is rooted in nothingness. He also says
we derive our concept of logical negation from this experience of
nothing. This suggests a privileged perspective for human beings.
We differ from animals with respect to nothing.

Since Heidegger thinks that animals do not experience nothingness, he is committed to skepticism about animal reasoning
involving negation. Consider the Stoic example of a dog that is
following a trail. The dog reaches a fork in the road, sniffs at one
road and then, without a further sniff, proceeds down the only
remaining road. The Stoics took this as evidence that the dog has
performed a disjunctive syllogism: “Either my quarry went down this
road or that road. Sniff—he did not go down this road.
Therefore, he went down that road.” Heidegger must discount this as
anthropomorphism.

Many biologists and psychologists side with the Stoic's emphasis on
our continuity with animals. They deny that human beings have a
monopoly on nothingness. A classic anomaly for the stimulus-response
behaviorist was the laboratory rat that responds to the absence of a
stimulus:

One rather puzzling class of situations which elicit fear are those
which consist of a lack of stimulation. Some members of this
class may be special instances of novelty. An anesthetised chimpanzee
could be described as a normal chimpanzee with the added novelty of
‘no movement’; solitude could be the novelty of ‘no
companions’. This is not simply quibbling with words; for there
is very good evidence (see Chapter 13) that the failure of a stimulus
to occur at a point in time or space where it usually occurs acts like
any other kind of novel stimulus. However, the intensity of the fear
evoked by the sight of a dead or mutilated body is so much greater
than that evoked by more ordinary forms of novelty that we perhaps
ought to seek an alternative explanation of the effects of this
stimulus. Fear of the dark is also difficult to account for in terms
of novelty, since by the time this fear matures darkness is no less
familiar than the light. (Gray 1987, 22)

These anomalies for behaviorism fill rationalists with mixed emotions.
On the one hand, the experiments refute the empiricist principle that
everything is learned from experience. On the other hand, the
experiments also constitute a caution against over-intellectualizing
absences. A
correct explanation of emotional engagement with absences must be more
general and cognitively less demanding than rationalists tend to
presuppose. Even mosquito larvae see shadows. Perhaps the earliest form
of vision was of these absences of light. So instead of being a pinnacle
of
intellectual sophistication, cognition of absences may be primal.

Existentialists tend to endorse the high standards assumed
by rationalists. Their disagreement with the rationalists is over whether the standards are met.
The existentialists are impressed by the contrast between our expectations of
how reality ought to behave and how it in fact performs.

This sense of absurdity makes existentialists more accepting
of paradoxes. Whereas rationalists nervously view paradoxes as a challenge to
the authority of reason, existentialists greet them as opportunities to correct
unrealistic hopes. Existentialists are fond of ironies and do
not withdraw reflexively from the pain of contradiction. They
introspect upon the inconsistency in the hope of achieving a
resolution that does justice to the three dimensionality of deep
philosophical problems. For instance, Heidegger is sensitive to the
hazards of saying that nothing exists. Like an electrician who must twist and
bend a wire to make it travel through an intricate hole, the metaphysician must
twist and bend a sentence to probe deeply into the nature of being.

What is to be investigated is being only and—nothing else; being
alone and further—nothing; solely being, and beyond
being-nothing. What about this Nothing? … Does the Nothing exist
only because the Not, i.e. the Negation, exists? Or is it the other
way around? Does Negation and the Not exist only because the Nothing
exists? … We assert: the Nothing is prior to the Not and the
Negation…. Where do we seek the Nothing? How do we find the
Nothing…. We know the Nothing…. Anxiety reveals the
Nothing…. That for which and because of which we were anxious,
was 'really'—nothing. Indeed: the Nothing itself—as such—was
present…. What about this Nothing?—The Nothing itself
nothings. (Heidegger as quoted by Carnap 1932, 69)

This paragraph, especially the last sentence, became notorious as a specimen of metaphysical nonsense.

The confusion caused by Heidegger's linguistic contortions is exacerbated by
separating them from their original text and herding them into a crowded pen. But there is a difference
between a failure to understand and an understanding of failure. The real test
for whether Heidegger's sentences are meaningless is to see what can be made of them in
action, applied to the questions they
were designed to answer.

Carnap also needs to consider the possibility that Heidegger's
sentences are illuminating nonsense. After all, Carnap was
patient with the cryptic Wittgenstein. In the Tractatus,
Wittgenstein speaks
like an oracle. He even
characterized his carefully enumerated sentences as rungs in a ladder
that must be cast away after we have made the ascent and achieved an
ineffable insight. And Wittgenstein meant it,
quitting philosophy to serve as a lowly schoolmaster in a rural village.

Other critics deny that What is Metaphysics? suffers from an
absence of meaning. Just the reverse: they think Heidegger's passages
about nothing involve too many meanings. When Heidegger
connects negation with nothingness and death, these logicians are put
in mind of an epitaph that toys with the principle of excluded middle:
Mrs Nott was Nott Alive and is Nott Dead. According to these
critics, Heidegger's writings can only be understood in the way we
understand the solution to equivocal riddles:

What does a man love more than life?
Hate more than death or mortal strife?
That which contented men desire,
The poor have, the rich require,
The miser spends, the spendthrift saves,
And all men carry to their graves?

(Leemings, 1953, 201)

The answer, Nothing, can only be seen through a kaleidoscope
of equivocations.

Some of the attempts to answer ‘Why is there something rather
than nothing?’ equivocate or lapse into meaninglessness. The
comedic effect of such errors is magnified by the fundamentality of
the question. Error here comes off as pretentious error.

Those who ask the question ‘Why is there something rather
than nothing?’ commonly get confused. But the question
itself appears to survive tests for being
merely a verbal confusion.

In any case, the question (or pseudo-question) has helped to hone the diagnostic
tools that have been applied to it. As the issue gets shaped and re-shaped by
advances in our understanding of ‘is’, quantification and explanatory standards, it becomes
evident that the value of these diagnostic tools is not exhausted by
their service in exposing pseudo-questions. For genuine questions become better
understood when we can discriminate them from their spurious look-alikes.